Cut the stems away from the eggplant and slice off the ends. Use a mandolin on the widest setting to slice the eggplant, lengthwise, into slices between ¼ and ½-inch thick. Or, use a sharp knife and a steady hand to slice them as uniformly as possible.
Layer the slices in a colander set over a plate, sprinkling each layer with salt. Let stand for 30 minutes to drain.
Meanwhile, in a bowl, stir together the ricotta, mozzarella, 2 tablespoons Parmesan, parsley, ½ tsp salt, and a pinch of black pepper. Set aside.
Preheat your oven to 450°F.
Line a large baking sheet (or 2 smaller ones) with parchment paper. Spray the parchment paper with cooking spray.
Rinse the eggplant slices under cold running water to remove the salt. Pat each eggplant layer dry with paper towels.
Brush the slices on both sides with olive oil, and arrange them in a single layer on a baking sheet.
Bake the slices until lightly browned, about 10 minutes.
Turn the slices and continue to bake until browned on the second side and nice and tender, 8 minutes longer. Remove from the oven and immediately lower the oven temperature to 350°F.
Ladle marinara into the baking dish. Fill the bottom so there is enough to snuggle the rollatini into the sauce.
To make each eggplant roll, place a spoonful of the cheese mixture near one end of a slice and roll up the slice.
As each roll is formed, place it seam side down in the dish.
Spoon more sauce over the rolls.
Sprinkle with more grated Parmesan.
Bake the rolls until the sauce is bubbling hot and the rolls are heated through, about 20 to 25 minutes. Remove from the oven, garnish with chopped fresh parsley, and serve at once.